Problem: Which of the following numbers is a factor of 153? ${4,7,8,9,10}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $153$ by each of our answer choices. $153 \div 4 = 38\text{ R }1$ $153 \div 7 = 21\text{ R }6$ $153 \div 8 = 19\text{ R }1$ $153 \div 9 = 17$ $153 \div 10 = 15\text{ R }3$ The only answer choice that divides into $153$ with no remainder is $9$ $ 17$ $9$ $153$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $9$ are contained within the prime factors of $153$ $153 = 3\times3\times17 9 = 3\times3$ Therefore the only factor of $153$ out of our choices is $9$. We can say that $153$ is divisible by $9$.